....If everybody will ignore it, then what purpose it will serve, aside from drastically increasing the size of the output image?
On the other hand, on Amiga, there is no alpha channel, even the graphic cards supports only 24-bit bitmaps...

Everybody (every tool) unfamilar with this chunk will ignore it(!). Note the difference. Think about the future. You want to have a future for your tool, aint you?
Well, your tool can have an option to include/exclude that alpha?? Maybe a 1bit-alpha (mask!)?
Why not create an entire new image class, likewise iff24?

Why should a user care about image's filesize anyway? This is not 1995 anymore!
Make it an option. Design it wisely. Publish the specifications.
The DataType will follow.
(This is how it would work on Amiga).
Btw. gfx cards supports any 24 bit image, which could also be a composition of many different sources of images, therefore also a combined color+alpha image. it is not the hardware that defines the src image.